Further energy saving (hereinafter, simply called energy saving) has been demanded for a railway with excellent energy efficiency, due to power shortage in recent years. That is, the energy saving in a railway is to change an auxiliary machine such as air-conditioning and lighting to an equipment with excellent energy efficiency, and to reduce energy at the time of running of a train, and so on. Particularly, the energy saving at the time of running of a train has been considered since long ago, and it has variously been discussed in the reference documents listed below.
Generally, the following three policies are taken in many cases, in the energy saving relating to an operation of a train.
(1) To accelerate a train at a maximum acceleration at the time of departing from a departure station.
(2) To preferably increase coasting (inertia running) within a speed limitation.
(3) To decelerate a train at a maximum deceleration at the time of reaching a station.
Regarding these fundamental policies, various energy saving running curve creation methods have been proposed so far. In order to create a running curve based on these fundamental policies, many methods to create a running curve by a heuristic have been proposed. However, in a case that a speed limitation is simple such as one maximum speed exists between stations, and in a case that a running time is larger compared with a shortest time, a running curve close to an optimum running curve can be obtained even by a heuristic. However, in a case that the speed limitation between stations is complicated, when a running curve is created by a heuristic, there is a case that a solution cannot be obtained, or only a solution may be obtained in which the energy consumption is considerably larger than an optimum solution. For the reason, a method which can obtain a solution close to an optimum solution has been desired, even if a given speed limitation and gradient are complicated.